Integração Vertical em Telecomunicações e Fechamento Através de Preços de Acesso
César Mattos1
Resumo
É conhecido na literatura de economia da regulação os incentivos que uma
empresa verticalmente integrada no setor de telecommunicações, proprietária das redes
local e de longa distância, possui de fechar este último mercado para concorrentes
demandantes de interconexão. Isso ocorreu no mercado de telecomunicações americano,
dada a dependência dos novos concorrentes na longa distância (MCI e Sprint) nas redes
de acesso locais da AT&T que possibilitariam conexão com usuários finais. Objetivando
evitar estes problemas e introduzir concorrência pelo menos no segmento de longa
distância, a reforma das telecomunicações no Brasil seguiram muito proximamente a
experiência americana no processo antitruste que resultou na quebra da AT&T em 1984,
reduzindo a verticalização prévia da estatal TELEBRAS antes da privatização. Há uma
extensa literatura econômica sobre a idéia de fechamento vertical. Grande parte desta
literaturase concentra na idéia de uma integração vertical entre firmas nos segmentos à
jusante e à montante do mercado gerando um resultado de fechamento. Neste artigo,
focamos mais diretamente a questão do incumbente monopolista verticalmente integrado
decidindo preços de acesso cobrados ao rival entrante no segmento de longa distância.
Apresentamos dois modelos referentes à idéia de fechamento vertical em telecomunicações
através dos preços de acesso no contexto de um oligopólio de Cournot e Bertrand com
demanda e funções custo lineares. Ambos modelos indicam o mesmo resultado: Utilizando
uma definição apropriada do que significa fechamento vertical através de preços de
acesso, esse fenômeno não ocorre nestes modelos. Este se constitui em um resultado
surpreendente tando em vista o apelo intuitivo da idéia mais geral de fechamento vertical o
qual confirma a intuição da escola de Chicago da década de setenta relacionada a esta
idéia. O ponto relevante é que o incumbente verticalmente integrado pondera os impactos
do fechamento sobre o seu negócio de longa distância tanto quanto em seu negócio de
acesso. Em determinadas circunstâncias, será preferível fazer lucros pela provisão de
acesso do que operar ele próprio o serviço de longa distância. Em particular, não há um
viés sistemático do incumbente verticalmente integrado contra o entrante comparado ao
monopolista provedor de acesso. Assim, chega-se à conclusão que o fechamento vertical
através de preços não deveria ser tomado como uma justificativa razoável para a
estratégia de quebra vertical da TELEBRAS e mesmo na experiência antitruste dos EUA.
Palavras-chave: concorrência, fechamento vertical, telecomunicações, preços de
acesso.
Vertical Integration in Telecommunications and Foreclosure Through Access Prices
Abstract
1
Departamento de Economia - Universidade de Brasília – UNB.
2
It is known in regulatory economics the incentive that a vertically integrated
company in the telecommunications sector, owning a local and a long distance network,
has to foreclose interconnecting competitors in the long distance market in its local loop
bottleneck. This occurred in the US telecommunications market, given the dependence of
the new long distance competitors (MCI and Sprint) on the AT&T local networks to
connect with end users. Aiming to avoid these problems and introduce competition at least
in the long distance segment, the telecom reform in Brazil followed closely the US antitrust
experience in the AT&T divestiture of 1984, reducing the previous verticalization of the
state-owned company TELEBRAS before privatization. There is an extensive economic
literature on the idea of vertical foreclosure. Most of this literature concentrate on the idea
of a vertical merger between firms in the downstream and upstream markets generating
foreclosure. We aim to focus more directly in the issue of a vertically integrated incumbent
deciding access prices to the entrant rival in the long distance segment. We present two
models that refer to vertical foreclosure in telecommunications through access prices in the
context of Cournot and Bertrand competition with simple linear demand and cost functions.
Both indicate the same thing: Under a suitable definition of what means vertical
foreclosure through prices, this phenomena does not happen. This is a surprising result in
view of the intuitive appeal of the idea behind vertical foreclosure and confirms at least in
part the intuition of Chicago’s view in the seventies related to this idea. The relevant point
is that the vertically integrated incumbent weights the impact of foreclosure in his
downstream segment as well as in his access business. In certain circumstances, it will be
better to make profits by providing access rather than by operating by himself in the long
distance. In particular, there is not a systematic bias of the vertically integrated incumbent
against the entrant compared to an independent monopolist access provider. So, we find
that vertical foreclosure through prices should not be taken as a suitable justification for
the strategy of vertical break-up of TELEBRAS and even for the vertical break-up of AT&T.
Key-words: competition, vertical foreclosure, telecommunications, access pricing.
ANPEC: Área 04 - Microeconomia, Economia Industrial e Mudança Tecnológica e
Métodos Quantitativos
JEL: L12, L22, L42
3
Introduction
The incentive that a vertically integrated company owning a local and a long
distance network in telecommunications has to foreclose interconnecting competitors from
the long distance market in its local loop bottleneck is a known phenomena in
telecommunications. This occurred in the US telecommunications market, given the
dependence of the new long distance competitors (MCI and Sprint) on the AT&T local
networks to connect with end users. In the US antitrust trial that resulted in the vertical
break-up of AT&T in 1984, the company was charged of using its market power to reduce
downstream competition, raising rival costs through refusal to deal, high local
interconnection charges and reduction of the quality of access2. In the UK, these problems
also appeared after the privatization of British Telecom (BT), which is usually attributed to
the absence of a policy of vertical break-up as implemented in the antitrust suit in the US3
and the lack of appropriate action by OFTEL4. The long distance service reform in Brazil
followed closely the US antitrust experience in the AT&T divestiture of 19845, reducing the
previous verticalization of the state-owned company, TELEBRAS6.
The theoretical rationale behind this behaviour rests on the economics of vertical
foreclosure. A vertically integrated incumbent owning the local service bottleneck and the
long distance service will use its ownership of the essential facility represented by the local
service to get rid of its competitors in the long distance, mainly refusing to deal and/or
charging a very high access price to the latter. While intuitive and very used in the antitrust
literature, this simple idea was under severe attack from the theoretical point of view and
has received relevant transformations as time goes by. Furthermore, as we will see below,
the literature is more concerned in assessing vertical mergers than to address the most
2
Viscusi, Vernon and Harrington (VVH-1995, p. 504/505) summarize the history of AT&T negotiations with
MCI about the requests for local network interconnection: “The initial response of AT&T to entry in 1969 by
MCI was simply to refuse to interconnect with them. In the FCC decision in 1971, the FCC said AT&T should
interconnect with their competitors, but the terms were left open to AT&T. This did not improve the situation,
because AT&T placed considerable restrictions on the specialized common carriers. Only on 1974 did the
FCC order interconnection in its Bell System Tariff Offering decision. When MCI expanded entry into
message toll service, the same problem arose. Their entry was approved by the US court of appeals in 1975,
but not until 1978 was AT&T forced to interconnect with MCI’s Execunet service.Only in 1978 were firms
like MCI allowed to interconnect with the local operating company as long lines. Even after achieving this
right, the competitors to AT&T in the Intercity Telecommunication Market were still not treated equally. It is
generally believed that AT&T’s competitors were given poorer quality connections by Bell operating
companies. Customers had to dial twenty digits to make a long distance call with MCI, but only eleven with
AT&T. The result was that consumers saw AT&T as offering a higher-quality product, which forced its
competitors to offer a discount to compete. It was this type of behaviour that led to the original antitrust suit
against AT&T”.
3
The lack of vertical break-up is also found in the Canadian experience as shown by Crandall and Waverman
(1995,p. 67/68).
4
According to Armstrong, Cowan and Vickers (1994, p. 239) “Mercury should be protected against
anticompetitive behavior by BT, and it is unfortunate that resolution of the question of interconnection was
held up for as long as it was...”.
5
This was considered the largest antitrust settlement of all history and started in November, 1974 lasting
almost 10 years until full implementation.
6
It is worthwhile to mention that the USA instituted a more radical vertical break-up compared to Brazil. See
Mattos (2001).
4
simple case of an already established vertically integrated incumbent that faces a new
entrant in the potentially competitive long distance segment.
The purpose of this article is to define vertical market foreclosure through access
prices from the perspective of an established vertically integrated incumbent facing entrants
and show through a Cournot and a Bertrand models the incentive that the former has to
foreclose or not. We will see that, according to the Chicago’s tradition, the two models
point for the complete absence of vertical foreclosure if we adopt a suitable definition for
this phenomena.
In the next section, we provide a survey of the literature on the vertical foreclosure
issue in the economic literature. Sections 3 and 4 present, respectively, the Cournot and
Bertrand models of vertical foreclosure. Section 5 concludes.
2) The Economics of Vertical Foreclosure: A Survey
There are two main theories behind any antitrust intervention in vertical integrations
in the US: i) entry barriers and ii) “market foreclosure” or “essential-facility” doctrine.
The entry barrier theory is based on the fact that vertical integration may increase
the capital requirements for another firm to enter the market7. Following this rationale in
the case of denial of access to the incumbent local loop, every long distance carriers would
have to enter also the local distance service to be able to provide long distance service. This
could make the cost to compete in the long distance service prohibitively high8.
The market foreclosure idea remains as the most important rationale for antitrust
intervention on vertical merger and potentially anticompetitive practices. Rey and Tirole
(1997,p.1) state the fundamentals of the “market foreclosure” reasoning in the antitrust
literature and jurisprudence:
“According to the received definition, foreclosure refers to any dominant firm’s
practice that denies proper access to an essential input it produces to some users of this
input, with the intent of extending monopoly power from one segment of the market (the
bottleneck segment) to the other (the potentially competitive segment). The excluded firms
on the competitive segment are than said to be “squeezed” or to be suffering a secondary
line injury. Essentiality means that the dominant firm’s product cannot cheaply be
7
According to Perry (1989, p. 197), this theory was originally conceived with the first body of theoretical
work related to the concept of barriers to entry of Bain in 1956.
8
The barrier of entry theory brings the presumed anticompetitive effects of the vertical merger under the more
general idea coming from the Bain tradition that any large expenditure necessary to start up a business is a
barrier to entry. The main criticism of this general view and thus to the view that a vertical merger creates or
increases as a barrier to entry was by Posner (1979) as quoted by VVH (1995, p. 160):“Suppose that it costs $
10,000,000 to build the smallest efficient plant to serve some market; then, it was argued, there is a
$10,000,000 “barrier to entry”, a hurdle a new entrant would have to overcome to serve the market at no
disadvantage vis-à-vis existing firms. But is there really a hurdle? If the $ 10,000,000 plant has a useful life
of, for example, tem years, the annual cost to the new entrant is only $1,000,000. Existing firms bear the same
annual cost, assuming that they plan to replace their plants. The new entrant, therefore, is not at any cost
disadvantage at all”.
5
duplicated by users who are denied access to it. Examples of essential facilities or
bottlenecks to which competition law has been applied include a stadium, a railroad bridge
or station, a harbor, a power transmission or a local telecommunications network, and a
computer reservation system. The foreclosure or essential facility doctrine states that the
owner of an essential facility may have an incentive to monopolize complementary or
downstream segments as well. This doctrine was first discussed in the United States in
Terminal Railroad Association v. U.S. (1912), in which a set of railroads formed a joint
venture owning a key bridge across the Mississipi river and the approaches and terminal in
Saint Louis and excluded non-member competitors”.
In the case of AT&T, the local loop was considered an essential facility given the
difficulty of duplication by competitors, mainly because of its natural monopoly
characteristics.
The foreclosure theory was severely criticised by the Chicago school, mainly
through the writings of Bork (1978) and Posner (1976)9 that argued the lack of economic
rationality for firms to reckon with a vertical merger strategy to raise their profits, by
foreclosing the market. For these authors, the single explanation for vertical integration
would be the generation of efficiencies. Rey and Tirole (1997, p. 7) summarises the
Chicago criticism:
“The thrust of the Chicago School critique of this doctrine is that there is only one
final product market and therefore only one monopoly power to be exploited, and that it is
not obvious how the monopolist could further extend its monopoly power”.
Given the lack of rationality to exclusionary behaviour in the foreclosure approach,
these authors defended the intrinsic efficiency aspects of the vertical mergers. The force of
this criticism resulted in a decrease of tightness of the antitrust policy toward vertical
mergers in the US10. Indeed, there are many critiques of the foreclosure theory. Surveyed
by Ordover, Saloner and Salop (1990, p. 128/129), one of these critiques can be applied to
the essential facility case of an integrated company owning a bottleneck like the telecom
local network case. According to these authors, this critique relates to the fact that “..lost
upstream profits” due to downstream competitor foreclosure “may exceed the increased
downstream profits” of the integrated firm and thus there would be no reason to foreclose.
As we will see in our models below, this effect holds in our models.
The emergence of these critiques was mainly due to the lack of a rigorous analysis
of the economic rationality of vertical foreclosure. Several authors started to provide more
9
See Comanor (1969) for a full critique of the foreclosure idea as well. This author (p. 259) argues that
“although vertical integration may well have the important effect of extending high concentration levels from
one stage of production to another, it cannot be held responsible for high concentration prior to integration.
And it is the latter that results in market power which is exercised through vertical relationships”. The main
point for this author was that the degree of market power would not be “additive at successive stages” which
is the core of the Chicago critique.
10
See Perry (1989,p. 244/247) for a brief history of the whole legal evolution of the vertical merger control in
the US until that time. The Clayton act did not apply to vertical mergers until 1950, when it was amended by
the Celler-Kefauver act.
6
rigorous economic rationales, improving the understanding of the possible economic
reasoning behind foreclosure11, escaping from the naive leverage version of the theory that
was used by the US courts until the seventies. Tirole (1988, p.193/198) provides a survey
of these efforts from the end of the seventies up to the publication of his textbook. One
important aspect that emerged is that socially inefficient market foreclosure could be
obtained through a myriad of generic strategies aiming to raise rival costs12 including
exclusionary vertical long term contracts13 rather than only vertical mergers. Concerning
the issue of market foreclosure by vertical integration, Tirole (p. 195) states that, with few
exceptions, the main failure of the economic literature was not explaining why integrated
firms do not sell or buy on the intermediate goods market instead of foreclosing. The two
exceptions were published afterwards on the papers of Salinger (1988) and Ordover,
Saloner and Salop (1990).
Salinger (1988) shows that the vertically integrated firm after the merger does not
participate in the upstream input market but only supply its downstream associated
company, foreclosing the access of other downstream firms. Ordover, Saloner and Salop
(1990) structure a model where vertical foreclosure can emerge as an equilibrium in a
successive duopoly setting. The model is a four-stage game where the final equilibrium is
obtained through backward induction. The main importance of the paper is that it replies
the six main criticisms against the foreclosure doctrine14. The main result of their model is
that the vertical merger hurts both downstream companies. At the same time, both upstream
firms are benefited and the consumer is unambiguously hurt, since final price always
increases. The full structure of the game results in the two downstream firms facing a
prisoner dilemma regarding who will be the first to integrate15.
Hart and Tirole (1990) build a rich and complex set of hypotheses under which
foreclosure can emerge16. The model consists of two potential suppliers at the upstream and
11
According to Rey and Tirole (1997,p. 4): “The Chicago school view has had the beneficial effect of forcing
industrial economists to reconsider the foreclosure argument and to put it, we believe, on firmer ground”.
12
See Salop and Scheffman (1983). Salop and Scheffman (1987) extend the basic model of 1983 to other
situations, including the one where a dominant integrated firm prefers not to produce their own inputs more
efficiently and buy more expensive inputs in the market aiming to raise the rival costs. Anyway, in this case,
the vertical integration is not the source of foreclosing behavior. See also Salop and Kratenmark (1993).
13
The most known model of exclusive dealing arrangement that forecloses inefficiently the market comes
from Aghion and Bolton (1987), also summarised by Tirole (1988 p.196/198). The model replies formally the
criticisms from Bork (1978) and Posner (1976) that criticized the decision of the courts in the exclusionary
contracts of the case United Shoe Machinery Corporation of 1922 on the basis that there was not any
incentive for the buyers to feed a monopoly on the other side of the market, signing contracts that exclude
competitors.
14
The first stage of the game happens when both downstream firms bid to acquire one of the upstream
suppliers. In the second stage, input prices are determined. As one of the bidding downstream companies
acquire one upstream firm, the other downstream firm bids to acquire the remaining supplier in the third
stage. Finally, downstream prices are chosen in the fourth stage.
15
The authors summarize this intuition stating that “the fear of being foreclosed drives each firm to attempt to
foreclose the other. As a result, all the rents from foreclosure are dissipated through the bidding and all the
profits accrue to the upstream firm(s)”.
16
As in the former model of Salinger (1988), foreclosure can occur, but total welfare can still increase. In
other words, foreclosure is not a necessary condition to justify antitrust intervention based on welfare
grounds.
7
two potential buyers at the downstream level deciding or not to merge vertically in a
strategic way, i.e., whether considering what they think the other pair of
upstream/downstream firms may do in response to a vertical merger. Three variants of the
basic model are constructed: a) ex post monopolization is the single variant that results in
output contraction, being the most closely connected to the usual intuition of the antitrust
authorities; b) scarce needs where the downstream firms face capacity constraints and the
main reasoning for vertical integration is the need of one of the upstream firms to ensure
that the downstream firm purchases its supplies and not from the rival’s.; c) scarce supplies
where the upstream firms face capacity constraints and the main reasoning for the vertical
merger is the need of one of the downstream firm to ensure that the upstream firm channels
its scarce supplies to it instead to the other downstream firms17. There are a variety of
possible outcomes within each one of these three variants. This derives mainly from the
incorporation in the model of two potential gains from mergers, that are i) avoidance of
wasteful facility duplication (investment costs) by the remaining firms and ii) pure
efficiency gains, which include the elimination of an eventual hold-up problem on the
merged firm investment. When the investments are relationship specific rather than
industry specific, holdup problems are relevant and, thus, efficiency considerations18 may
be balanced. However, the incentive to merger for assuring scarce supply or demand
implying foreclosure in Hart and Tirole’s model increases as well and thus net impact on
welfare is ambiguous.
The model of Rey and Tirole (1997) provides a rationale for the foreclosure theory
closer to the first variant of the Hart and Tirole (1990) model. But differently from the 1990
model, this one explicitly relates the market foreclosure idea to the known Coase model of
the “durable good” monopolist. Rey and Tirole (p.10/17) show that the bottleneck facility
owner facing oligopolists in the complementary market may not be able to credibly commit
that he will maintain the monopoly result in the contracts with each of these players. This
result can be obtained with the bottleneck monopolist offering to each of the oligopolists a
“take it or leave it” contract that specifies the quantity supplied and the total remuneration.
The upstream firm always has an ex-post incentive to open secret renegotiations, acting
opportunistically against the downstream contractors. Anticipating this result, each
downstream oligopolist does not accept the contracts that ensues the monopoly result for
the upstream bottleneck. This represents a decrease on the bottleneck monopolist’s profit.
There are two main ways to deal with this problem: an exclusive dealing
arrangement with one of the oligopolist or a merge. In both cases, the bottleneck
monopolist refuses to deal with the others, foreclosing the market. In this case, the
17
Perry (1989, p. 206/208) presents a brief survey of the earlier literature on the assurance of supply argument
mainly summarizing the important model of Carlton (1979). This paper of Hart and Tirole seems to be the
first one to link more explicitly the argument of assurance of supply with the market foreclosure result. Bolton
and Whinston (1993) almost simultaneously build another model resting on the same basic reasoning of Hart
and Tirole (1990), but on a multilateral (and not bilateral) context. The authors conclude that “transaction
costs saving are often a two-wedged sword, with the alleviation of supply assurance concerns for merging
parties often exacerbating supply assurance concerns for other downstream firms and leading to a form of
market foreclosure”.
18
In the traditional line of Williansom (1975, 1985), Klein, Crawford and Alchian (1978) and Grossman and
Hart (1986).
8
temptation for opportunistic behaviour is eliminated. The monopolist bottleneck is able to
extract all monopolist rents from the complementary market and the chosen downstream
firm will not fear about opportunistic behaviour. In this regard, the result is a departure
from the conventional wisdom since foreclosure does not aim to extend market power from
one market to another, but rather reestablish the market power from a situation where the
oligopolists in the complementary market fear the opportunistic behaviour from the
bottleneck monopolist.
In the case of the relationship between long distance carriers and the local loop
bottleneck in telecommunications, this problem is not so sharp. The Coasean problem
applied to this bottleneck facility framework is more acute when the bottlenecks are at more
upstream levels and far from the direct contact with the consumer. This happens because
when the monopolist is at the interface with the consumer, he is more inclined to internalise
negative externalities between oligopolists (p.18). Therefore, as in the case of the local loop
the monopolist is directly responsible for the connection with the customer, this source of
incentive to foreclose is reduced. However, though it reduces foreclosure concerns, the
location of the bottleneck monopolist at the interface with the final consumers decreases
welfare (p.25), given that his ability to charge monopoly prices is greater.
More recently, Kuhn and Vives (1999), extending and formalizing a conjecture
raised by Perry (1989), link the foreclosure caused by vertical integration and the “excess
entry” result from Mankiw and Whinston (1986) arising from the “business stealing effect”.
In their model, foreclosure brings down the number of players in the market more in line to
the social optimum. Thus, vertical integration by increasing foreclosure and hurting
competitors can increase efficiency and social welfare.
The “excess entry result” was also addressed by Vickers (1995) in the context of the
linkages between a natural monopoly market with a potentially competitive one. The
novelty of his analysis for our purpose is the introduction of price regulation at the
monopolistic level, mainly access regulated prices, considering the information asymmetry
of the regulator. This is a crucial departure from the previous literature on foreclosure and
applies more closely to the situation of the regulated sectors, including telecommunications.
The basic trade-off of the cost and benefits of keeping vertical integration is stressed by the
author (p. 4):
“Vertical integration has the disadvantage that the regulator’s task is made harder
insofar as the monopolist has incentives to raise rivals’ costs, but it may have the
advantage of offsetting excess entry and hence allowing a more efficient production
structure in the competitive industry”.
The “efficiency” effect comes directly from saving fixed costs. The author also
show that when the firm in the bottleneck level is allowed to enter the competitive level
(vertical integration), the optimal regulated access price is higher, increasing the market
share of the vertical integrated firm and decreasing their average cost. This shows that if the
target is to avoid foreclosure, even regulated interconnection prices are not perfect
substitutes for vertical separation to avoid some degree of market foreclosure strategy.
9
The models described above represent the core of the current literature on
foreclosure. However, almost all of them (with the exception of Vickers’ model) are
focused on the effects of vertical mergers and not on the more simple idea that an already
integrated firm owning an essential facility will (or will not) often have an incentive to
foreclose supply to downstream competitors.
We construct some models to address this simple question. In these models, the
problem of the upstream monopolist commitment explored by Rey and Tirole (1997) is
meaningless, since one upstream firm and one downstream firm are already working
together as a single firm. There are no capacity constraints on either sides of the market as
in Hart and Tirole (1990), since we suppose fixed marginal costs. There is not downstream
prisoners dilemma as in Ordover, Salop and Saloner (1990) and there is no need to suppose
the same assumptions of Salinger (1988). The model does not requires less than perfect
information of the regulator as in Vickers (1995).
3) Foreclosure Through Access Prices in a Cournot Model
To study vertical foreclosure through prices, we can first define this phenomena in a
broader sense, since full foreclosure is a particular and extreme case of a general case of
discrimination of a vertically integrated incumbent against an entrant.
The first candidate rule to obtain a proper definition would be the access market
price differential with marginal access cost. However, since the provision of access is also a
business, we can expect that even an independent non-integrated bottleneck supplier will
charge access prices greater than the marginal access cost. So, the access price/marginal
cost differential does not only capture the incentive of a vertically integrated incumbent to
protect its own downstream business, but also its incentive to make positive profits in the
access business. Thus, we have to pick a definition that eliminates this “access business
profit-seeking” effect that will occur regardless of vertical integration. This is made through
the following definition:
Definition 1- There is partial vertical foreclosure through access pricing from the
upstream bottleneck segment to a downstream potentially duopolistic segment, when both
downstream competitors have the same efficiency, but there is a positive access price
differential between the situation where the upstream access provider is a vertically
integrated firm and the situation where the access provider is an independent nonintegrated access supplier that is able to price discriminate in his access business and
faces the same number of downstream firms from the first situation.
Since the access price of the independent access provider will contain an access
business profit-seeking effect, differently from the marginal access cost, the differential
between the access price of the vertically integrated firm and the independent provider will
isolate for the effect of the ownership of the upstream access provider in the access price
rule, capturing for the vertical foreclosure incentive.
10
Note that the source of the bias could also stem from an efficiency differential and
not from vertical integration. That is why, we restrict the comparison to the case of equal
efficiency (equal marginal cost).
Furthermore, it is important to allow for the independent access provider to price
discriminate whenever he wishes. We will come back for the motivation behind this
hypothesis ahead.
The requirement of the independent supplier facing the same number of
downstream firms avoids potential differences associated to a different number of
downstream firms, not directly related to the incentives for vertical foreclosure.
Suppose a vertically integrated monopolist incumbent facing an entrant in the
downstream market. Assume that the entrant is not able to enter the local service
(upstream) if he did not enter the long distance service yet1920. The inverse demand function
and the profit functions of the upstream (1u) and downstream (1d) segments of the
incumbent firm and the entrant firm (2d) in the long distance business are given,
respectively, by:
P(q1 + q2 ) = 1 − q1 − q2
∏1u (q1 , q 2 ) = (a − c)(q1 + q 2 )
∏1d (q1 , q 2 ) = q1 (1 − q1 − q 2 ) − C1 (q1 )
∏ 2 d (q1 , q2 ) = q2 (1 − q1 − q2 ) − C 2 (q2 )
(1)
(2)
(3)
(4)
Variable qi is the quantity traded by the downstream firm i (i=1d,2d). C1(q1) and
C2(q2) are the total costs, respectively, of the incumbent and entrant downstream firms. a is
the access price charged by the upstream incumbent, 1u for both downstream firms 1d and
2d. We suppose that one unit of access results in one unit of long distance service provided
and there are no fixed costs at all. The parameter c is the marginal cost of the upstream firm
providing any input (access) quantity qi to the downstream firms. The expressions for the
total costs of the downstream firms are:
C1 (q1 ) = aq1 + c1 q1
C 2 (q 2 ) = aq 2 + c 2 q 2
(5)
(6)
The parameters c1 and c2 are the constant marginal costs of each downstream firm.
As the upstream firm is integrated with the downstream 1d, their profits must be
aggregated. Notice that when we derive the aggregate profit function of the vertically
integrated incumbent, the terms including the access price a cancel out in the sum. This is a
revenue to the upstream firm but an expense to the downstream firm. The profit equation of
the vertically integrated and entrant firms are, respectively
19
We can suppose that the marginal cost of the entrant, given that he does not operate in the long distance, is
infinity. The role of this assumption is to force the dependence of the entrant in the long distance to the
incumbent local network in the short run.
20
For the sake of simplicity, we also restrict to the case of two downstream companies and not “n”.
11
∏1 = q1 (1 − q1 − q2 ) + aq2 − c(q1 + q2 ) − c1q1
(7)
∏ 2 = q 2 (1 − q1 − q 2 ) − (a + c 2 )q 2
(8)
The oligopolists play a Cournot-Nash game in the downstream market. Given the
parameters of this game, the vertically integrated incumbent chooses the optimal value of
the access price a that he charges the entrant. We assume that the parameters are such that
there are only interior solutions. The reaction functions of both companies in the
downstream market are given by:
∂ ∏1
= 1 − 2q1 − q 2 − c − c1 = 0
∂q1
q1 =
1 − c − c1 − q 2
2
(9)
and
∂ ∏2
= 1 − 2q 2 − q1 − c − c 2 = 0
∂q 2
q2 =
1 − a − c 2 − q1
2
(10)
Solving for q1 and q2, we get:
1 + a − 2c1 − 2c + c 2
3
1 + c − 2c 2 − 2a + c1
q2 * =
3
q1 * =
(11)
The profit of the vertically integrated incumbent replacing (11) in (7) and (8) will be
given by :
(1 + a − 2c1 − 2c + c 2 ) (1 + c − 2c 2 − 2 a + c1 )
(1 + a − 2c1 − 2c + c 2 )
−
− c1 − c ]
[1 −
3
3
3
(1 + c − 2c 2 − 2 a + c1 )
+ (a − c)
3
∏1 =
12
∂ ∏1 2 (1 + a − 2c1 − 2c + c 2 ) (1 + c − 2c 2 − 2a + c1 ) 2(a − c)
=
+
−
=0
∂a
3
3
3
3
5 10a c1 5c 4c 2
−
− + −
9
9
9 9
9
1 c1 c 2c 2
a* = − + −
2 10 2
5
(12)
Next, we have to compare the optimal access price of the vertically integrated firm
given in (12) with that from an independent access supplier. There are two possibilities.
First, the independent access provider cannot price discriminate and settles the same access
price a to both downstream companies. Second, the independent access provider is able to
price discriminate and settles different access prices to each of the two downstream firms.
Note, however, that the vertically integrated firm is implicitly supposed to price
discriminate between the access price settled to the entrant (given in 12) and the access
price settled to himself (c by definition). If we do not allow price discrimination for the
independent access provider, the comparison of the access price he settles and the access
price of the vertically integrated firm given in (12) can be reflecting this asymmetry. In
other words, besides foreclosure, there would be also the effect of the ability to price
discriminate of the vertically integrated firm not possessed by the independent provider.
That is why we made explicit the possibility of price discrimination in the definition of
foreclosure above. So, a1 is the access price settled by the upstream firm to the downstream
firm 1 and a2 the access price settled to the downstream firm 2.
Next, we restate (2), (7) and (8) for the case of an independent access supplier in the
upstream with two companies in the downstream segment of the market:
∏1u = (a1 − c)q1 + (a 2 − c)q 2
∏1 = q1 (1 − q1 − q 2 ) − a1 q1 − c1 q1
∏ 2 = q 2 (1 − q1 − q 2 ) − a 2 q 2 − c 2 q 2
(2´)
(7´)
(8´)
Differentiating (7´) and (8´), respectively, with respect to q1 and q2, and solving the
system, we get:
1 + a 2 + c 2 − 2a1 − 2c1
q1 =
3
(11´)
1 + a1 + c1 − 2a 2 − 2c 2
q2 =
3
The independent access supplier incorporates (11´) in his problem (2´) and chooses
optimally a1 and a2:
1 + a 2 + c 2 − 2a1 − 2c1
1 + a1 + c1 − 2a 2 − 2c 2
∏1U = (a1 − c)[
] + (a 2 − c)[
]
3
3
13
∂ ∏1U 1 + a 2 + c 2 − 2a1 − 2c1 2
1
=
− (a1 − c) + (a 2 − c) = 0
∂a1
3
3
3
a1 =
1 + 2a 2 + c 2 − 2c1 + c
4
Given the symmetry of the problem:
a2 =
1 + 2a1 + c1 − 2c 2 + c
4
Solving for a1 and a2, we get:
1 − c1 + c
2
1 − c2 + c
a2 * =
2
The difference between (12) and (12´) (only a2*) is:
a1 * =
1 c c1 2c 2 1 c 2 c c 2 − c1
+ − −
− + − =
2 2 10
5
2 2 2
10
(12´)
(13)
So, the vertically integrated firm settles an access price that is greater than the
access price picked by an independent provider if and only if he is more efficient than the
entrant. Equation (13) results in Proposition 1.
Proposition 1: Given a downstream duopoly playing a Cournot game with the
linear demand function (1) and variable linear cost functions in the downstream
((a1+c1)q1 and (a2+c2)q2) and upstream segments (c(q1+q2)), there will be no incentive for
vertical foreclosure by the incumbent against an entrant through access pricing as
defined in Definition 1 resulting from a vertical integration of one of the downstream
firms and the upstream firm.
This matches the Chicago intuition, but with further insights. What equation (13) is
saying is that when the incumbent is less efficient than the entrant, the former tends to
charge a lower access price compared to what would charge an independent access
provider. This occurs because when the vertically integrated incumbent is less efficient, he
loses twice if he discriminates against the entrant: First, he does not extract a higher amount
of profits from the most efficient player and, second, he derives a lower amount of profits
through his own (less efficient) downstream subsidiary. On the other hand, the independent
access provider loses just once if he discriminates against the most efficient entrant, by not
extracting a higher amount of profits from the most efficient player. By the same token, the
vertically integrated incumbent earns twice when his downstream subsidiary is more
efficient. So, the vertically integrated incumbent is more sensitive to the cost differential
than the independent access provider. But this is not a vertical foreclosure strategy as
14
defined in definition 1. Discrimination occurs when the reduction in the upstream profits by
discriminating against the entrant is lower than the gains in the downstream market and this
just happens when the entrant is less efficient than the downstream subsidiary of the
incumbent.
The Chicago’s view is right by stating that the incumbent earn more in some
circumstances by providing access than by foreclosing and thus it is not so obvious that the
latter conduct should always be expected. Note, however, that this statement cannot be
taken as universal since the model here developed is restricted to specific linear demand
and cost functions. Checking how general is this finding is an interesting topic for further
research.
4) Foreclosure Through Access Prices in a Bertrand Model
Suppose now that the dowsntream competitors play a Bertrand instead of a Cournot
game. Assume that the downstream demand curve is given by (1).
We assume that c2 can be different from c1. In this case, prices will equal the highest
“total marginal cost” in equilibrium in the long distance downstream segment. Total
marginal cost equals the individual marginal cost ci plus the access price settled by the
upstream subsidiary of the vertically integrated incumbent a. So, the vertically integrated
incumbent controls part of the marginal cost of his downstream rival (a+c2) through the
access price settled by the upstream subsidiary and take as given his own marginal cost
(c+c1).
We have three hypothesis:
If
a + c 2 > c + c1
(Hypothesis 1)
P
hip1
Then, in a Bertrand equilibrium
= a + c2
(14)
In this case, only the vertically integrated incumbent produces, given that the access
price is very high and his profit will be:
∏11 = (a + c 2 − c)Q(a + c 2 )
(15)
Now, suppose that
a + c 2 < c + c1
(Hypothesis 2)
Then, in a Bertrand equilibrium
15
P hip 2 = c + c1
(16)
In this case, just the downstream entrant produces. The vertically integrated
incumbent gives up from his downstream operation and operates in the long distance only
providing access. The profit of the vertically integrated incumbent will be:
∏12 = (a − c)Q(c + c1 )
(17)
In the third hypothesis, we have:
a + c 2 = c + c1
⇒ a = c + c1 − c 2
(Hypothesis 3)
And the vertically integrated incumbent settles the access price exactly at the level
that establishes the equality above. This means that both produce and we suppose that they
divide the downstream market in the same proportion. The profit of the vertically integrated
firm will be:
∏13 = (c + c1 − c)
(c1 −
Q(c + c1 )
Q(c + c1 )
+ (c + c1 − c 2 − c)
=
2
2
c2
)Q(c + c1 )
2
(18)
Notice that we can drop hypothesis 2 where the entrant produces alone. Comparing
∏13 (18) with ∏12 (17), we have that
∏12 > ∏13 ⇔ (a − c) > c1 −
⇔ c + c1 < a +
c2
2
c2
2
(Condition 1)
This is the condition that defines whether the vertically integrated incumbent prefers
to fix access price such that hypothesis 2 holds instead of hypothesis 3. But note that under
hypothesis 2,
a + c 2 < c + c1
a contradiction with condition (1), since c2 is always non-negative. So, hypothesis 2
will never occur in this setting, since the vertically integrated incumbent will never prefer
to pick a such that hypothesis 2 holds. So, he will never leave the entrant alone in the
market.
16
Therefore, we are restricted to compare hypothesis 1 and 3. For this purpose, we
have to find the optimal access price settled by the vertically integrated incumbent in
hypothesis 1:
∏11 = (a + c 2 − c)Q (a + c 2 ) =
(a + c 2 − c)(1 − a − c 2 )
(15´)
∂ ∏11
= 1 − a − c 2 − a − c2 + c = 0
∂a
1 − 2c 2 + c
a* =
2
(19)
The profit of the vertically integrated incumbent under hypothesis 1 (just the
downstream subsidiary of the vertically integrated incumbent operating) will be:
1 − 2c 2 + c
(1 − 2c 2 + c)
(1 − c) (1 − c) (1 − c) 2
(
+ c 2 − c)(1 −
− c2 ) =
=
2
2
2
2
4
(20)
The profit of the vertically integrated incumbent under hypothesis 3 with both
producing will be:
∏13 = (c1 −
c2
)(1 − c − c1 )
2
(18´)
Next, we have to address what will be the optimal access price settled by the
vertically integrated incumbent, given the profit functions described above under
hypothesis 1 and 3. So, if
c
(1 − c) 2
> (1 − c − c1 )(c1 − 2 )
4
2
(Condition 2)
the vertically integrated incumbent prefers to produce alone and does not even offer
access to the entrant. Note that as 1>c+c1, this will not occur only if the downstream
incumbent is sufficiently more inefficient than the downstream entrant (or c1 is sufficiently
greater than c2/2).
Next, we address the problem of the independent access provider. He settles access
price a1 to downstream firm 1 and a2 to downstream firm 2. There are also three hypothesis.
First,
a1 + c1 < a 2 + c 2
(Hypothesis 4)
17
In this case, given Bertrand competition, only firm 1 produces at price a2+c2.
Analogously, if
a1 + c1 > a 2 + c 2
(Hypothesis 5)
Then, only firm 2 produces at a1+c1. And if
a1 + c1 = a 2 + c 2
(Hypothesis 6)
both downstream companies produce. We would like to argue that the single
equilibrium for the independent access provider will be that established by hypothesis 6.
Intuitively, the independent access provider will always wish to curb the downstream
market power and avoid losing profits in a typical double marginalization problem. For
instance, suppose that the fourth hypothesis holds (a1+c1<a2+c2). Then, firm 1 is the single
operator in the Bertrand game and will settle its price at a2+c2. Given the negative slope of
the demand curve, if the independent access provider reduces a2 to something infinitely
close to a1+c1-c2, the price settled by firm 1 has to reduce, the quantity sold increases and
the profit of the former increases. Formally, the problem of the independent access
provider, under the fourth hypothesis, is
∏1i = (a1 − c)(1 − a 2 − c 2 )
Such that
a1 + c1 ≤ a 2 + c 2
(21)
Then, the function to be maximized is
∏1ik = (a1 − c)(1 − a 2 − c 2 ) + λ (a 2 + c 2 − a1 − c1 )
(21´)
Kuhn-tucker conditions are:
18
∂ ∏1ik
a1 = (1 − a 2 − c 2 − λ )a1 = 0
∂a1
∂ ∏1ik
a 2 = (− a1 + c + λ )a 2 = 0
∂a 2
∂ ∏1ik
λ = (a 2 + c 2 − a1 − c1 )λ
∂λ
If we focus exclusively in interior (non-zero) solutions for a1 and a2, we have that:
λ = 1 − a 2 − c 2 = a1 − c
(22)
Note that it would be non-sense for the independent access provider to settle a1=c
and gives up all the profits from the access business. So, λ>0 and from the third first-order
condition:
a1 * +c1 = a 2 * +c 2
(23)
and then, we show that the constraint of problem (20) is binding and hypothesis (6)
holds.
So, we assume that the independent access supplier provides access to both
companies and chooses simultaneously the optimal access prices to both under a constraint
given by hypothesis (6):
(1 − a1 − c1 )
(1 − a1 − c1 + c 2 − c 2 )
+ (a1 + c1 − c 2 − c)
=
2
2
(1 − a1 − c1 )
(2a1 + c1 − 2c − c 2 )
2
∏ u = (a1 − c)
(24)
A first-order condition is:
∂ ∏ u 2(1 − a1 − c1 ) − 2a1 − c1 + c 2 + 2c
=
=0
∂a1
2
2
a1 * =
2 − 3c1 + c 2 + 2c
4
(25)
and by analogy
2 + c1 − 3c 2 + 2c
a2 * =
4
(26)
Since, there is no likelihood of the vertically integrated incumbent leaving the whole
downstream market to the entrant in a Bertrand setting as we saw before, we address two
19
scenarios. The comparison of the access price of firm 2, 1) when just firm 1 produces in the
context of a vertically integrated incumbent and an independent access provider and 2)
when both produce.
In the first case (just firm 1 produces), there will be vertical foreclosure if:
2 + c1 − 3c 2 + 2c 1 − 2c 2 + c
<
⇒
4
2
c1 + c 2 < 0
(condition 3)
which never holds since c1 and c2 are always non-negative.
So, in a Bertrand setting, we can also say that there is no vertical foreclosure
through access pricing like in the Cournot setting.
In the second period, there will be vertical foreclosure if
c + c1 − c 2 >
2 + c1 − 3c 2 + 2c
4
3
c + c1 − c 2 > 1
2
for c1=c2
Condition 4
Making c1=c2, condition 4 becomes:
c1
>1
2
But we know that for the production to be feasible, 1> c+c1, which is not
compatible with condition 4. So, there is also no vertical foreclosure in this second case.
Now, we are able to change Proposition 1 in the following sense.
c+
Proposition 1’: Given a downstream duopoly playing a Cournot or a Bertrand
game with the linear demand function (1) and variable linear cost functions in the
downstream ((a1+c1)q1 and (a2+c2)q2) and upstream segments (c(q1+q2)), there will be no
incentive for vertical foreclosure by the incumbent against an entrant through access
pricing as defined in Definition 1 resulting from a vertical integration of one of the
downstream firms and the upstream firm.
The proof about the non-existence of vertical foreclosure through prices in the case
of Bertrand competition is not so simple as in the case of Cournot, but unambiguously
points to the same direction: There is no vertical foreclosure through access prices in these
models under the assumptions established above.
20
The non-foreclosure result under Bertrand competition is even stronger than in the
Cournot case. The point is that Bertrand competition is tougher than Cournot. The price of
the active player, even playing alone in the market, is, in average, more constrained than in
the case of Cournot. So, the vertically integrated incumbent will earn relatively less in the
downstream business playing Bertrand compared to a Cournot game. At the same time,
lower prices mean higher quantities and more profits carried to the access business in the
upstream segment. This makes the access business relatively more attractive than the final
service business for the vertically integrated incumbent in the Bertrand case. On the other
hand, the independent access provider does not have this choice of switching from the
downstream to the upstream and vice-versa and disregards the fact that the downstream
final service business is less profitable in a Bertrand setting. Then, once more and even
representing a stronger result, there is no foreclosure in the case of a Bertrand oligopoly.
5) Conclusions
Though not quite general, both models sketched above show that under the main
oligopoly models of the economic theory (Cournot and Bertrand) and under a suitable
definition of what means vertical foreclosure, this phenomena does not happen. In this
regard, it is possible that the concerns of vertical foreclosure through access prices can be
overestimated at least when we consider the linear models adopted here.
The reason for this behaviour in the two models are distinct. In the case of Cournot
competition, the result of non-foreclosure depends crucially on the hypothesis made in
definition 1 above that comparisons must be made for players with equal efficiency. The
vertically integrated incumbent is more sensitive to efficiency differences but does not have
any bias against the entrant. This occurs because the vertically integrated incumbent loses
twice if he departs from the rule picked by the independent access provider as explained in
section 3 above. In the case of Bertrand oligopoly, this effect is even stronger since
competition makes, even in the absence of the rival in the market, the downstream service
market relatively less attractive than the access business.
There are two important disclaimers. First, the results do not mean that access price
regulation is not required, but only that vertical foreclosure through access prices fails to
occur. Thus, access price regulation will be justified on the grounds of monopoly theory,
but not on the vertical integration of the incumbent. Second, if there is not vertical
foreclosure in these two models, it does not mean that we cannot find some other oligopoly
structure where vertical foreclosure through prices can occur. More than that, we restrained
to address vertical foreclosure through prices. As we showed in another work21, it is
possible to find suitable economic models where vertical foreclosure is a rational response
when the control variable is quality, mainly when the fear of the incumbent in being taken
over in the local service in the long run is present.
Finally, the results of this paper indicate that vertical foreclosure through access
prices do not look a suitable motivation to justify the strategy of breaking-up TELEBRAS
21
See Mattos (2001).
21
into local and long distance services. Other rationales for vertical foreclosure have to be
sought.
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